Definitely not a bike guy. That had to have been someone's pride and joy once upon a time.

Cosmetically, evaporust or oxalic acid followed by chrome polish will likely make that look acceptable. The chainstays are pretty bad though. I'd consider a rechrome and repaint down the road, if you really like the bike, and plan to keep and ride it yourself. As you probably already know, when rust is removed like this, it doesn't actually repair the damage. What you really are doing is polishing the underlying steel so that you don't easily notice the chrome is gone in spots, and it can easily rust again if not kept after.